Question
The cost of an item is 'A'. A
shopkeeper increases the price by 'x'%, then applies a discount of 'd'% on the increased price. After applying the discount, the final price returns to 'A'. If 'd' represents the difference between 'x' and 'd', determine the value of 'x'. I) 50 II) 100 III) 200Solution
ATQ, Given x% of CP = d% of MP I.e. x% of 'A' = d% of MP --- (1) Also Given, d = d-x, then x = 0 which is [not possible as A < MP and not A = MP] So, d = x-d x = 2d & d = x/2 Now from options check in which option overall change is 0, i.e. CP= SP & x - d -xd/100 = 0 Option I: x= 50 then d= 25 Here, x - d -xd/100 = 50-25-[50×25]/100 = 12.5 So here CP is not equal to SP & x - d -xd/100 is not equal to 0. Option II: x= 100 then d= 50 Here, x - d -xd/100 = 100-50-[50×100]/100 = 0 So option II is the correct option
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